Nowadays the impulse measurements are taking on higher importance. This is because by means of current impulses it is possible to measure at high currents and low power loading conditions without overheating the sample or measurement equipment. In this article, we present a system enabling to measure current-voltage curves of superconducting tapes with high critical currents and in overcritical current conditions. In our measurements, the current impulses are quasi trapezoidal and include a ramp increase, a plateau and a long ramp decrease. The complete current impulse duration is of the order of ten milliseconds, though the plateau (useful part for the measurement) is of sub-millisecond range. The current derivative in the plateau is zero. Thus, this conditions are comparable with DC ones. A special ladder transmission line was used as high-current generator for shaping impulses with instantaneous currents up to 1.5 kA. A DAQ system with a sampling rate up to 100 kS/s and 24 bits resolution was used for the measurement. The signal processing was realized by software. This method using quasi trapezoidal current impulses was compared with the method of measurement by means of impulses without plateau. Measured current-voltage curves compared with curves obtained by DC measurements are presented, showing a very good agreement.